Regular characters of classical groups over complete discrete valuation rings

Let $\mathfrak{o}$ be a complete discrete valuation ring with finite residue field $\mathsf{k}$ of odd characteristic, and let G be a symplectic or special orthogonal group scheme over $\mathfrak{o}$. For any $?\in \mathbb{N}$ let $G^{?}$ denote the ?-th principal congruence subgroup of $\mathbf{G}(\mathfrak{o})$. An irreducible character of the group $\mathbf{G}(\mathfrak{o})$ is said to be regular if it is trivial on a subgroup $G^{?+1}$ for some ?, and if its restriction to $G^{?}/G^{?+1}?\mathrm{Lie}(\mathbf{G})(\mathsf{k})$ consists of characters of minimal $\mathbf{G}({\mathsf{k}}^{\mathrm{alg}})$-stabilizer dimension. In the present paper we consider the regular characters of such classical groups over $\mathfrak{o}$, and construct and enumerate all regular characters of $\mathbf{G}(\mathfrak{o})$, when the characteristic of $\mathsf{k}$ is greater than two. As a result, we compute the regular part of their representation zeta function.     

Synthesis of α-fluoro-α,β-unsaturated esters monitored by 1D and 2D benchtop NMR spectroscopy

For optimization and control of pharmaceutically and industrially important reactions, chemical information is required in real time. Instrument size, handling, and operation costs are important criteria to be considered when choosing a suitable analytical method apart from sensitivity and resolution. This present study explores the use of a robust and compact nuclear magnetic resonance (NMR) spectrometer to monitor the stereo-selective formation of α-fluoro-α,β-unsaturated esters from α-fluoro-β-keto esters via deprotonation and deacylation in real time. These compounds are precursors of various pharmaceutically active substances. The real-time study revealed the deprotonation and deacylation steps of the reaction. The reaction was studied at temperatures ranging from 293 to 333 K by interleaved one-dimensional ¹H and ¹⁹F and two-dimensional ¹H–¹H COSY experiments. The kinetic rate constants were evaluated using a pseudo first-order kinetic model. The activation energies for the deprotonation and deacylation steps were determined to 28 ± 2 and 63.5 ± 8 kJ/mol, respectively. This showed that the deprotonation step is fast compared with the deacylation step and that the deacylation step determines the rate of the overall reaction. The reaction was repeated three times at 293 K to monitor the repeatability and stability of the system. The compact NMR spectrometer provided detailed information on the mechanism and kinetics of the reaction, which is essential for optimizing the synthetic routes for stepwise syntheses of pharmaceutically active substances.     

An adaptive multilevel wavelet framework for scale‐selective WENO reconstruction schemes

We put forth a dynamic computing framework for scale‐selective adaptation of weighted essential nonoscillatory (WENO) schemes for the simulation of hyperbolic conservation laws exhibiting strong discontinuities. A multilevel wavelet‐based multiresolution procedure, embedded in a conservative finite volume formulation, is used for a twofold purpose. (i) a dynamic grid adaptation of the solution field for redistributing grid points optimally (in some sense) according to the underlying flow structures, and (ii) a dynamic minimization of the in built artificial dissipation of WENO schemes. Taking advantage of the structure detection properties of this multiresolution algorithm, the nonlinear weights of the conventional WENO implementation are selectively modified to ensure lower dissipation in smoother areas. This modification is implemented through a linear transition from the fifth‐order upwind stencil at the coarsest regions of the adaptive grid to a fully nonlinear fifth‐order WENO scheme at areas of high irregularity. Therefore, our computing algorithm consists of a dynamic grid adaptation strategy, a scale‐selective state reconstruction, a conservative flux calculation, and a total variation diminishing Runge‐Kutta scheme for time advancement. Results are presented for canonical examples drawn from the inviscid Burgers, shallow water, Euler, and magnetohydrodynamic equations. Our findings represent a novel direction for providing a scale‐selective dissipation process without a compromise on shock capturing behavior for conservation laws, which would be a strong contender for dynamic implicit large eddy simulation approaches.     

A framework to perform high-order deconvolution for finite-volume method on simplicial meshes

In this article, a new framework to design high-order approximations in the context of node-centered finite volumes on simplicial meshes is proposed. The major novelty of this method is that it relies on very simple and compact differential operators, which is a critical point to achieve good performances in the High-performance computing context. This method is based on deconvolution between nodal and volume-average values, which can be conducted to any order. The interest of the new method is illustrated through three different applications: mesh-to-mesh interpolation, levelset curvature computation, and numerical scheme for convection. Higher order can also be achieved within the present framework by introducing high-rank tensors. Although these tensors feature much symmetries, their manipulation can quickly become an overwhelming task. For this reason and without loss of generality, the present articles are limited to third-order expansion. This method, although tightly connected to the k-exact schemes theory, does not rely on successive corrections: the high-order property is obtained in a single operation, which makes them more attractive in terms of performances.     

基于特征正交分解的一类瞬态非线性热传导问题的新型快速分析方法

提出了一种基于特征正交分解(POD)和有限元法的瞬态非线性热传导问题的模型降阶快速分析方法, 建立了导热系数随温度变化的一类瞬态非线性热传导问题有限元格式的POD降阶模型. 在隐式时间推进方法的基础上有效结合单元预转换方法和多级线性化方法发展了一种加速求解瞬态非线性热传导降阶模型的新型计算方法,并通过二维和三维算例验证了该方法的准确性和高效性. 研究结果表明: (1)降阶模型解的均方根误差在经过初始时段轻微的脉动后稳定于0.01%以下, 而其计算效率比有限元全阶模型提高2$\sim $3个数量级, 并且自由度数量(DOFs)愈大提高的幅度也愈加显著; (2)新型算法解决了常规算法在计算非线性降阶模型时加速性能差的问题, 即使是在DOFs比较小的时候也能够明显提高计算效率; (3)常数边界条件下得到的POD模态可以用来建立相同求解域在各种复杂时变边界条件下的瞬态非线性热传导降阶模型, 并对其传热过程和温度场进行快速准确的分析与预测, 具有很好的工程应用价值.      

Experimental Performance of a Solid Heat Exchanger with Tree-Like Flow Passages

System performance of a solid single-fluid compact heat exchanger with tree-like flow passages has been experimentally examined. The results, presented in the form of commonly defined dimensionless parameters, demonstrate that system performance can be characterized in a mode similar to traditional compact heat exchanger designs. Pressure forces were found to dominate inertia forces at low Reynolds numbers. Correlations of the Euler number, Nusselt number, Colburn factor, and friction factor as a function of Reynolds number were utilized to compare system performance to traditional two-fluid compact heat exchangers.     

A study of the effect of step excrescences and free‐stream disturbances on boundary layer stability

In this work, a study of the mechanism by which free‐stream acoustic and vorticity disturbances interact with a boundary layer flow developing over a flat plate featuring a step excrescence located at a certain distance from a blunt leading edge is included. The numerical tool is a high‐fidelity implicit numerical algorithm solving for the unsteady, compressible form of the Navier–Stokes equations in a body‐fitted curvilinear coordinates and employing high‐accurate compact differencing schemes with Pade‐type filters. Acoustic and vorticity waves are generated using a source term in the momentum and energy equations, as opposed to using inflow boundary conditions, to avoid spurious waves that may propagate from boundaries. The results show that the receptivity to surface step excrescences is largely the result of an overall adverse pressure gradient posed by the step, and that the free‐stream disturbances accelerate the generation of instabilities in the downstream. As expected, it is found that the acoustic disturbance interacting with the surface imperfection is more efficient in exciting the Tollmien–Schlichting waves than the vorticity disturbance. The latter generates Tollmien–Schlichting waves that are grouped in wave packets consistent with the wavelength of the free‐stream disturbance. Copyright © 2015 John Wiley & Sons, Ltd.     

大豆脲酶诱导碳酸钙沉淀的多因素影响分析

本文探究了多个影响因素对大豆脲酶诱导碳酸钙沉淀(SICP)的影响,以优选出主要影响因素并提供其最佳范围。首先分析了脲酶浓度和温度对脲酶活性的影响;之后通过正交实验设计,进行25种工况的SICP水溶液实验,研究不同因素组合下Ca²⁺利用率的变化规律;最后借助扫描电子显微镜观测不同工况下生成碳酸钙的形态。结果表明:低温有利于脲酶的保存及活性发挥,5 ℃时脲酶活性能保持21 d以上;同一温度下,脲酶浓度越大,脲酶初始活性越高,脲酶完全失活所需时间越短。pH值、脲酶与胶结液体积比是影响Ca²⁺利用率的主要因素。为达到较高的Ca²⁺利用率,脲酶和胶结液最佳体积比为1,氯化钙与尿素最佳浓度比为1.5,Ca²⁺最佳浓度为1 mol/L。当脲酶浓度较低时生成的六面体状碳酸钙较多;随着脲酶浓度的增大,所沉淀的碳酸钙向球形转变。大豆中富含的天冬氨酸是控制碳酸钙形态的重要因素。